메뉴 건너뛰기




Volumn 101, Issue 2, 2010, Pages 589-622

Spectral properties of the Cauchy process on half-line and interval

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77956292829     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1112/plms/pdq010     Document Type: Article
Times cited : (68)

References (47)
  • 1
    • 2942668409 scopus 로고    scopus 로고
    • The Cauchy process and the Steklov problem
    • R. Bañuelos and T. Kulczycki, 'The Cauchy process and the Steklov problem', J. Funct. Anal. 211 (2004) 355-423.
    • (2004) J. Funct. Anal. , vol.211 , pp. 355-423
    • Bañuelos, R.1    Kulczycki, T.2
  • 2
    • 33750883367 scopus 로고    scopus 로고
    • Spectral gap for the Cauchy process on convex symmetric domains
    • R. Bañuelos and T. Kulczycki, 'Spectral gap for the Cauchy process on convex symmetric domains', Comm. Partial Differential Equations 31 (2006) 1841-1878.
    • (2006) Comm. Partial Differential Equations , vol.31 , pp. 1841-1878
    • Bañuelos, R.1    Kulczycki, T.2
  • 4
    • 0000561344 scopus 로고
    • Maxima of sums of random variables and suprema of stable processes
    • N. H. Bingham, 'Maxima of sums of random variables and suprema of stable processes', Probab. Theory Related Fields 26 (1973) 273-296.
    • (1973) Probab. Theory Related Fields , vol.26 , pp. 273-296
    • Bingham, N.H.1
  • 5
    • 84972491111 scopus 로고
    • The asymptotic distribution of the eigenvalues for a class of Markov operators
    • R. M. Blumenthal and R. K. Getoor, 'The asymptotic distribution of the eigenvalues for a class of Markov operators', Pacific J. Math. 9 (1959) 399-408.
    • (1959) Pacific J. Math. , vol.9 , pp. 399-408
    • Blumenthal, R.M.1    Getoor, R.K.2
  • 7
    • 0000760840 scopus 로고
    • On the distribution of first hits for the symmetric stable processes
    • R. M. Blumenthal, R. K. Getoor and D. B. Ray, 'On the distribution of first hits for the symmetric stable processes', Trans. Amer. Math. Soc. 99 (1961) 540-554.
    • (1961) Trans. Amer. Math. Soc. , vol.99 , pp. 540-554
    • Blumenthal, R.M.1    Getoor, R.K.2    Ray, D.B.3
  • 8
    • 0002020384 scopus 로고    scopus 로고
    • Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
    • K. Bogdan and T. Byczkowski, 'Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains', Studia Math. 133 (1999) 53-92.
    • (1999) Studia Math , vol.133 , pp. 53-92
    • Bogdan, K.1    Byczkowski, T.2
  • 9
    • 77956275320 scopus 로고    scopus 로고
    • Heat kernel of fractional Laplacian in cones
    • K. Bogdan and T. Grzywny, 'Heat kernel of fractional Laplacian in cones', Colloq. Math. 118 (2010) 365-377.
    • (2010) Colloq. Math. , vol.118 , pp. 365-377
    • Bogdan, K.1    Grzywny, T.2
  • 11
    • 68749083442 scopus 로고    scopus 로고
    • Bessel potentials, hitting distributions and Green functions
    • T. Byczkowski, J. Małecki and M. Ryznar, 'Bessel potentials, hitting distributions and Green functions', Trans. Amer. Math. Soc. 361 (2009) 4871-4900.
    • (2009) Trans. Amer. Math. Soc. , vol.361 , pp. 4871-4900
    • Byczkowski, T.1    Małecki, J.2    Ryznar, M.3
  • 12
    • 77952292884 scopus 로고    scopus 로고
    • Hitting half-spaces by Bessel-Brownian diffusions
    • to appear
    • T. Byczkowski, J. Małecki and M. Ryznar, 'Hitting half-spaces by Bessel-Brownian diffusions', Potential Anal., http://www.springerlink.com/ content/h346720387j31621/ to appear.
    • Potential Anal
    • Byczkowski, T.1    Małecki, J.2    Ryznar, M.3
  • 14
    • 77955474529 scopus 로고    scopus 로고
    • Heat kernel estimates for Dirichlet fractional Laplacian
    • to appear
    • Z. Q. Chen, P. Kim and R. Song, 'Heat kernel estimates for Dirichlet fractional Laplacian', J. Eur. Math. Soc., to appear.
    • J. Eur. Math. Soc.
    • Chen, Z.Q.1    Kim, P.2    Song, R.3
  • 15
    • 0031572650 scopus 로고    scopus 로고
    • Intrinsic ultracontractivity and conditional gauge for symmetric stable processes
    • Z. Q. Chen and R. Song, 'Intrinsic ultracontractivity and conditional gauge for symmetric stable processes', J. Funct. Anal. 150 (1997) 204-239.
    • (1997) J. Funct. Anal. , vol.150 , pp. 204-239
    • Chen, Z.Q.1    Song, R.2
  • 16
    • 23344440772 scopus 로고    scopus 로고
    • Two sided eigenvalue estimates for subordinate Brownian motion in bounded domains
    • Z. Q. Chen and R. Song, 'Two sided eigenvalue estimates for subordinate Brownian motion in bounded domains', J. Funct. Anal. 226 (2005) 90-113.
    • (2005) J. Funct. Anal. , vol.226 , pp. 90-113
    • Chen, Z.Q.1    Song, R.2
  • 17
    • 28144449119 scopus 로고    scopus 로고
    • Continuity of eigenvalues of subordinate processes in domains
    • Z. Q. Chen and R. Song, 'Continuity of eigenvalues of subordinate processes in domains', Math. Z. 252 (2006) 71-89.
    • (2006) Math. Z. , vol.252 , pp. 71-89
    • Chen, Z.Q.1    Song, R.2
  • 18
    • 84967728254 scopus 로고
    • The maximum of sums of stable random variables
    • D. A. Darling, 'The maximum of sums of stable random variables', Trans. Amer. Math. Soc. 83 (1956) 164-169.
    • (1956) Trans. Amer. Math. Soc. , vol.83 , pp. 164-169
    • Darling, D.A.1
  • 19
    • 2942634534 scopus 로고
    • The first exit time of a two-dimensional symmetric stable process from a wedge
    • R. D. DeBlassie, 'The first exit time of a two-dimensional symmetric stable process from a wedge', Ann. Probab. 18 (1990) 1034-1070.
    • (1990) Ann. Probab. , vol.18 , pp. 1034-1070
    • Deblassie, R.D.1
  • 20
    • 4043135243 scopus 로고    scopus 로고
    • Higher order PDE's and symmetric stable processes
    • R. D. DeBlassie, 'Higher order PDE's and symmetric stable processes', Probab. Theory Related Fields 129 (2004) 495-536.
    • (2004) Probab. Theory Related Fields , vol.129 , pp. 495-536
    • Deblassie, R.D.1
  • 21
    • 34547341496 scopus 로고    scopus 로고
    • α-continuity properties of the symmetric α-stable process
    • R. D. DeBlassie and P. J. Ḿendez-Herńandez, 'α-continuity properties of the symmetric α-stable process', Trans. Amer. Math. Soc. 359 (2007) 2343-2359.
    • (2007) Trans. Amer. Math. Soc. , vol.359 , pp. 2343-2359
    • Deblassie, R.D.1    Ḿendez-Herńandez, P.J.2
  • 23
    • 0004188078 scopus 로고
    • Springer, Berlin
    • E. B. Dynkin, Markov processes, vols. I and II (Springer, Berlin, 1965).
    • (1965) Markov Processes , vol.1-2
    • Dynkin, E.B.1
  • 27
    • 84972514239 scopus 로고
    • Markov operators and their associated semi-groups
    • R. K. Getoor, 'Markov operators and their associated semi-groups', Pacific J. Math. 9 (1959) 449-472.
    • (1959) Pacific J. Math. , vol.9 , pp. 449-472
    • Getoor, R.K.1
  • 29
    • 84976175704 scopus 로고
    • Short surface waves in the presence of a finite dock. I, II
    • 985-1011
    • R. L. Holford, 'Short surface waves in the presence of a finite dock. I, II', Math. Proc. Cambridge Philos. Soc. 60 (1964) 957-983, 985-1011.
    • (1964) Math. Proc. Cambridge Philos. Soc. , vol.60 , pp. 957-983
    • Holford, R.L.1
  • 30
    • 36749063550 scopus 로고
    • On some relations between the harmonic measure and the Ĺevy measure for a certain class of Markov processes
    • N. Ikeda and S. Watanabe, 'On some relations between the harmonic measure and the Ĺevy measure for a certain class of Markov processes', Probab. Theory Related Fields 114 (1962) 207-227.
    • (1962) Probab. Theory Related Fields , vol.114 , pp. 207-227
    • Ikeda, N.1    Watanabe, S.2
  • 31
    • 84968484961 scopus 로고
    • Random walks and a sojourn density process of Brownian motion
    • F. B. Knight, 'Random walks and a sojourn density process of Brownian motion', Trans. Amer. Math. Soc. 109 (1963) 56-86.
    • (1963) Trans. Amer. Math. Soc. , vol.109 , pp. 56-86
    • Knight, F.B.1
  • 32
    • 0742287284 scopus 로고    scopus 로고
    • The ice-fishing problem: The fundamental sloshing frequency versus geometry of holes
    • V. Kozlov and N. G. Kuznetsov, 'The ice-fishing problem: the fundamental sloshing frequency versus geometry of holes', Math. Methods Appl. Sci. 27 (2004) 289-312.
    • (2004) Math. Methods Appl. Sci. , vol.27 , pp. 289-312
    • Kozlov, V.1    Kuznetsov, N.G.2
  • 33
    • 0038434657 scopus 로고    scopus 로고
    • Intrinsic ultracontractivity for symmetric stable processes
    • T. Kulczycki, 'Intrinsic ultracontractivity for symmetric stable processes', Bull. Pol. Acad. Sci. Math. 46 (1998) 325-334.
    • (1998) Bull. Pol. Acad. Sci. Math. , vol.46 , pp. 325-334
    • Kulczycki, T.1
  • 34
    • 68749100739 scopus 로고    scopus 로고
    • Spectral gap estimate for stable processes on arbitrary bounded open sets
    • M. Kwásnicki, 'Spectral gap estimate for stable processes on arbitrary bounded open sets', Probab. Math. Statist. 28 (2008) 163-167.
    • (2008) Probab. Math. Statist. , vol.28 , pp. 163-167
    • Kwásnicki, M.1
  • 35
    • 76349112019 scopus 로고    scopus 로고
    • Spectral gap estimate for stable processes on arbitrary bounded open sets
    • M. Kwásnicki, 'Spectral gap estimate for stable processes on arbitrary bounded open sets', Semigroup Forum 79 (2009) 183-192.
    • (2009) Semigroup Forum , vol.79 , pp. 183-192
    • Kwásnicki, M.1
  • 36
    • 0036524696 scopus 로고    scopus 로고
    • Exit times from cones in Rn of symmetric stable processes
    • P. J. Ḿendez-Herńandez, 'Exit times from cones in Rn of symmetric stable processes', Illinois J. Math. 46 (2002) 155-163.
    • (2002) Illinois J. Math. , vol.46 , pp. 155-163
    • Ḿendez-Herńandez, P.J.1
  • 37
    • 0000944515 scopus 로고
    • Symmetric stable processes as traces of degenerate diffusion processes
    • S. A. Molchanov and E. Ostrowski, 'Symmetric stable processes as traces of degenerate diffusion processes', Theory Probab. Appl. 14(1) (1969) 128-131.
    • (1969) Theory Probab. Appl. , vol.14 , Issue.1 , pp. 128-131
    • Molchanov, S.A.1    Ostrowski, E.2
  • 38
    • 0000728524 scopus 로고
    • Expansions in generalized eigenfunctions of selfadjoint operators
    • T. Poerschke, G. Stolz and J. Weidmann, 'Expansions in generalized eigenfunctions of selfadjoint operators', Math. Z. 202 (1989) 397-408.
    • (1989) Math. Z. , vol.202 , pp. 397-408
    • Poerschke, T.1    Stolz, G.2    Weidmann, J.3
  • 39
    • 84972512714 scopus 로고
    • Sojourn times of a diffusion process
    • D. B. Ray, 'Sojourn times of a diffusion process', Illinois J. Math. 7 (1963) 615-630.
    • (1963) Illinois J. Math. , vol.7 , pp. 615-630
    • Ray, D.B.1
  • 42
    • 0011444297 scopus 로고
    • Int́egrales de Riemann-Liouville et potentials
    • M. Riesz, 'Int́egrales de Riemann-Liouville et potentiels', Acta Sci. Math. Szeged (1938).
    • (1938) Acta Sci. Math. Szeged
    • Riesz, M.1
  • 45
    • 84927465241 scopus 로고
    • Some theorems concerning 2-dimensional Brownian motion
    • F. Spitzer, 'Some theorems concerning 2-dimensional Brownian motion', Trans. Amer. Math. Soc. 87 (1958) 187-197.
    • (1958) Trans. Amer. Math. Soc. , vol.87 , pp. 187-197
    • Spitzer, F.1
  • 46
    • 0003207103 scopus 로고
    • Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals
    • Princeton University Press, Princeton, NJ
    • E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series 43 (Princeton University Press, Princeton, NJ, 1993).
    • (1993) Princeton Mathematical Series , vol.43
    • Stein, E.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.